Structural refinement types

Abstract

Static types are a great form of lightweight static analysis. But sometimes a type like List is too coarse – we would also like to work with its refinements like non-empty lists, or lists containing exactly 42 elements. Dependent types allow for this, but they impose a heavy proof burden on the programmer. We want the checking and inference of refinements to be fully automatic. In this article we present a simple refinement type system and inference algorithm which uses only variants of familiar concepts from constraint-based type inference. Concretely, we build on the algebraic subtyping approach and extend it with typing rules which combine properties of nominal and structural type systems in a novel way. Despite the simplicity of our approach, the resulting type system is very expressive and allows to specify and infer non-trivial properties of programs.